MTEL Math Practice Test: 20-23

TL;DR

Solve problems involving exponents, algebraic equations, and sales tax.

Transcript

Problem 20. The expression 5 to the minus 8 times 7 to the minus 9 is equal to which of the following? And here we see a bunch of answers. Let's see, where they have a 35 there. So I suspect that they want to have us somehow multiply the 5 times the 7. So let me write this in terms that I have an easier time understanding it. So, 5 to the minus 8 t... Read More

Key Insights

• ⚾ Negative exponents can be simplified by rewriting them as one over the base to the positive exponent.
• 🍹 The sum of numbers in a vertical rectangle in a given diagram is equal to the sum of numbers in a horizontal rectangle.
• 😫 An equation can be set up to find the number of blocks bought by considering the total cost with and without sales tax.

Questions & Answers

Q: How can we simplify the expression 5 to the minus 8 times 7 to the minus 9?

The expression can be simplified by rewriting it as 1 over 5 to the 8 times 1 over 7 to the 9, which is equal to 1 over 5 to the 8 times 7 to the 9. By rewriting 7 to the 9th power as 7 to the 8th power times 7, the expression becomes 1 over 5 to the 8 times 7 to the 8 times 7 or 5 times 7 to the 8th power. Therefore, the answer is B.

Q: How can we prove that the sum of numbers in the vertical rectangle is equal to the sum of numbers in the horizontal rectangle?

In the vertical rectangle, the sum of numbers is given by x minus 5 plus x plus x plus 5, which simplifies to 3x. In the horizontal rectangle, the sum of numbers is x minus 1 plus x plus x plus 1, which also simplifies to 3x. Therefore, the sum of numbers in the vertical rectangle is equal to the sum of numbers in the horizontal rectangle.

Q: What equation represents the total cost of buying blocks with sales tax included?

The equation is 1.05 times the price per block (p) times the number of blocks (x) plus 3 is equal to $315.

Q: What equation represents the amount of money the craft person receives for each item sold?

The equation is 0.6p minus 3, where p represents the sale price of one item.

Summary & Key Takeaways

• Problem 20 involves simplifying an expression with negative exponents and multiplying two numbers to find the correct answer choice.

• Problem 21 requires finding an algebraic equation that proves the sum of numbers in a vertical rectangle is equal to the sum of numbers in a horizontal rectangle in a given diagram.

• Problem 23 asks for an expression representing the amount of money the craft person receives when selling an item, taking into account the sales price, store fees, and sales tax.